Finite Group DatabasebetaFinite Group Databasebeta| order | 11421 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C34×C47 · Schur multiplier (H2) = C35 |
| direct product | C3×C47×#737 |
| subgroup | G/H | |
|---|---|---|
| center | C3×C9×C47 | C32 |
| commutator, Frattini, cosocle | C3 | C34×C47 |
| socle | C32×C47 | C33 |
| prime radical | C3×H(3,𝔽3)×C47 | C3 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C9×C47 ◁ G | |
480 conjugacy classes of subgroups.
4653 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11421, 64);